(56d) Stochastic Model Predictive Control for Central HVAC Plants

Commercial buildings are responsible for over 20% of the total energy consumption in the U.S. and annual expenditures of over $200 billion [1]. In this context, heating, ventilation and air-conditioning (HVAC) systems are the largest sources of energy use (nearly 50%) [2]. Central HVAC plants are sophisticated systems that connect multiple energy carriers (water, electricity, natural gas, cooling water, hot water, steam) and equipment units (pumps, heat exchangers, cooling towers, chillers, and boilers) to meet the cooling and heating loads of single buildings or collections of buildings (e.g., university campuses and urban districts) [3]. Besides total energy use, temporal profiles and peak use are also key factors that affect the efficiency and sustainability of energy infrastructures. In particular, temporal profiles and peaks might push infrastructures to their design limits (e.g., capacity and ramping) and this might force operators to use inefficient back-up systems. Time-varying market prices and demand charges are used by operators and utility companies to try to mitigate such impacts. These pricing structures create an incentive for HVAC plants to incorporate thermal energy storage (TES) in order to shift loads in time and manipulate peak demands [5, 6]. Effective operation of HVAC plants requires careful real-time management of the multiple components of the central plant; this is a challenging task because of the tight interconnection of equipment units, the presence of constraints, and the presence of multiple time-varying disturbances (e.g., energy loads and prices) that cannot be perfectly anticipated and thus complicate the planning process. All these factors are forcing commercial buildings to incorporate more sophisticated automation systems.

Model predictive control (MPC) is becoming an established automation technology in HVAC central plants [3, 7, 8]. MPC can anticipate and counteract disturbances and accommodate complex models, constraints, and cost functions [9]. However, existing MPC implementations for HVAC central plants use deterministic representations of the disturbances (e.g., mean forecasts obtained from autoregressive models) to compute control actions. Uncertainty associated with forecast errors is thus ignored during the computation of the control action and, instead, errors are counteracted through feedback. This deterministic approach is intuitive and works well in practice but might lead to cost degradation and failure to satisfy constraints [10]. Uncertainty can be explicitly captured in the controller formulations such as stochastic MPC [11, 12]. In the context of energy systems, it has been recently reported that stochastic MPC can systematically mitigate constraint violations and improve economic performance [10, 13]. The benefits of stochastic MPC have also been widely reported in the context of building climate (airside) control [14, 15] and energy management [16, 17], but these studies have focused on the building (airside) and the central HVAC plants.

In this work, we present a computational framework for stochastic MPC for central HVAC plants. Our framework addresses HVAC plants for university campuses and seeks to assess the benefits of stochastic MPC over deterministic MPC. The framework uses real disturbance data to conduct fore- casting and uncertainty quantification of disturbances. Our benchmarking procedure uses extensive closed-loop simulations under myriad realizations of disturbances in order to properly account for the effect of uncertainty in controller performance. Results indicate that deterministic MPC leads to violations of storage capacity constraints (overflow or drying up) of the hot and chilled water tanks and that stochastic MPC mitigates this issue. We find that storage capacity violations can be partially mitigated in deterministic MPC by adding buffer (back-off) terms but also that stochastic MPC consistently outperforms deterministic MPC in terms of cost. Specifically, we show that stochastic MPC achieves savings in total cost of up to 7.52%. When these savings are disaggregated, we find consistent reductions in electricity cost (of 6.89%), in peak demand charges (of 29.8%), in natural gas cost (of 8.57%). We also find that stochastic MPC achieves significant reductions in natural gas usage and thus provides an effective approach to manipulate both electricity and natural gas demand profiles.

References:

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